Finite Group Databasebeta

← C11×#10051 #14587244

Subgroups — C11×#10051 #14587244

Order 2816.

670 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#486C211yesmaximal, characteristic
2C2×C11×#460C211yesmaximal, characteristic
3C11×#2546C211yesmaximal, characteristic, complemented
4C11×#1982C211yesmaximal, characteristic
5C2×C11×#332C211yesmaximal, characteristic, complemented
6C2×C11×Q8⋊C8C211yesmaximal, characteristic, complemented
7C11×#1279C211yesmaximal, characteristic, complemented
8C22×C11×SD16—21no—
9C2×C11×C4⋊Q8—21no—
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C11×#127C2211yescharacteristic
12C2×C4×Q8×C11C2211yescharacteristic
13C11×#486—22no—
14C11×#486—22no—
15C11×#460—22no—
16C11×#460—22no—
17C2×C11×C4⋊C8C2211yescharacteristic
18C2×C11×C4⋊C8C2211yescharacteristic
19C2×C11×#102—21no—
20C2×C11×#102—22no—
21C2×C11×#102—22no—
22C2×C4×C8×C11C2211yescharacteristic
23C11×#398—22no—
24C11×#391—21no—
25C11×#389—22no—
26C4×C11×C4⋊C4C2211yescharacteristic
27C11×#332—22no—
28C11×Q8⋊C8—22no—
29C22×Q8×C11—21no—
30C22×Q8×C11D411yescharacteristic
31C22×D4×C11—21no—
32C22×D4×C11—21no—
33C22×D4×C11—21no—
34C2×C11×SD16—24no—
35C2×C11×SD16—42no—
36C2×C11×SD16—42no—
37C22×C8×C11—21no—
38C22×C8×C11—21no—
39C22×C8×C11—21no—
40C11×C4⋊Q8—21no—
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8—21no—
44C11×C4⋊Q8—42no—
45C11×C4⋊Q8—42no—
46C11×#127—21no—
47C11×#127—21no—
48C11×#127—21no—
49C11×#127D412yes—
50C4×Q8×C11—21no—
51C4×Q8×C11—21no—
52C4×Q8×C11—21no—
53C4×Q8×C11—21no—
54C2×C11×C4⋊C4—24no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4D411yescharacteristic
58C2×C11×C4⋊C4D412yes—
59C2×C11×C4⋊C4D412yes—
60C2×C42×C11—21no—
61C2×C42×C11—21no—
62C2×C42×C11C2311yescharacteristic
63C11×C4⋊C8—21no—
64C11×C4⋊C8—21no—
65C11×C4⋊C8—21no—
66C11×C4⋊C8D412yes—
67C11×#102—24no—
68C11×#102—28no—
69C11×#102—44no—
70C4×C8×C11—21no—
71C4×C8×C11D412yes—
72C11×#95—24no—
73C11×#95—21no—
74#10051C1111yesmaximal, characteristic, direct product factor, Sylow
75C24×C11—41no—
76C2×Q8×C11—21no—
77C2×Q8×C11—21no—
78C2×Q8×C11—21no—
79C2×Q8×C11—21no—
80C2×Q8×C11—21no—
81C2×Q8×C11—41no—
82C2×Q8×C11—41no—
83C2×Q8×C11—41no—
84C2×Q8×C11—41no—
85C2×Q8×C11—41no—
86C2×Q8×C11—41no—
87C2×Q8×C11D812yes—
88C2×D4×C11—22no—
89C2×D4×C11—22no—
90C2×D4×C11—22no—
91C2×D4×C11—44no—
92C2×D4×C11—41no—
93C2×D4×C11—41no—
94C2×D4×C11—41no—
95C2×D4×C11—41no—
96C2×D4×C11—42no—
97C2×D4×C11—41no—
98C2×D4×C11—41no—
99C2×D4×C11—41no—
100C2×D4×C11—42no—
101C22×C4×C11—22no—
102C22×C4×C11—21no—
103C22×C4×C11—21no—
104C22×C4×C11—22no—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C11×SD16—48no—
109C2×C8×C11—22no—
110C2×C8×C11—22no—
111C2×C8×C11—42no—
112C2×C8×C11—41no—
113C2×C8×C11—41no—
114C2×C8×C11—42no—
115C2×C8×C11—41no—
116C11×C4⋊C4—22no—
117C11×C4⋊C4—21no—
118C11×C4⋊C4—22no—
119C11×C4⋊C4—21no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—48no—
122C11×C4⋊C4—41no—
123C11×C4⋊C4—41no—
124C11×C4⋊C4—41no—
125C11×C4⋊C4—41no—
126C11×C4⋊C4SD1614yescomplemented
127C42×C11—41no—
128C42×C11—41no—
129C42×C11—41no—
130C42×C11—41no—
131C42×C11C2×D411yescharacteristic
132C42×C11C2×D411yescharacteristic
133C42×C11C2×D411yescharacteristic
134C42×C11#4111yescharacteristic
135C2×#486C2×C1111yescharacteristic
136C2×#460C2×C1111yescharacteristic
137#2546C2×C1111yescharacteristic, complemented
138#1982C2×C1111yescharacteristic
139C2×#332C2×C1111yescharacteristic, complemented
140C2×Q8⋊C8C2×C1111yescharacteristic, complemented
141#1279C2×C1111yescharacteristic, complemented
142C23×C11—42no—
143C23×C11—81no—
144C23×C11—82no—
145C23×C11—81no—
146C23×C11—82no—
147C23×C11#12011yescharacteristic
148Q8×C11—22no—
149Q8×C11—22no—
150Q8×C11—41no—
151Q8×C11—41no—
152Q8×C11—81no—
153Q8×C11—81no—
154Q8×C11—81no—
155Q8×C11—81no—
156D4×C11—44no—
157D4×C11—42no—
158D4×C11—42no—
159D4×C11—44no—
160D4×C11—82no—
161D4×C11—81no—
162D4×C11—81no—
163D4×C11—81no—
164D4×C11—81no—
165C2×C4×C11—22no—
166C2×C4×C11—22no—
167C2×C4×C11—24no—
168C2×C4×C11—41no—
169C2×C4×C11—42no—
170C2×C4×C11—41no—
171C2×C4×C11—42no—
172C2×C4×C11—41no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11#12011yescharacteristic
178C2×C4×C11#12011yescharacteristic
179C2×C4×C11#12111yescharacteristic
180C2×C4×C11#12111yescharacteristic
181C2×C4×C11#12111yescharacteristic
182C2×C4×C11#12711yescharacteristic
183C2×C4×C11C2×D811yescharacteristic
184C2×C4×C11C2×SD1612yes—
185C2×C4×C11#13511yescharacteristic
186C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
187C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
188C2×C4×C11#13712yes—
189C8×C11—42no—
190C8×C11—42no—
191C8×C11—81no—
192C22×SD16—21no—
193C2×C4⋊Q8—21no—
194C2×C4⋊Q8C22×C1111yescharacteristic
195C2×#127C22×C1111yescharacteristic
196C2×C4×Q8C22×C1111yescharacteristic
197#486—22no—
198#486—22no—
199#460—22no—
200#460—22no—
201C2×C4⋊C8C22×C1111yescharacteristic
202C2×C4⋊C8C22×C1111yescharacteristic
203C2×#102—22no—
204C2×#102—21no—
205C2×#102—22no—
206C2×C4×C8C22×C1111yescharacteristic
207#398—22no—
208#391—21no—
209#389—22no—
210C4×C4⋊C4C22×C1111yescharacteristic
211#332—22no—
212Q8⋊C8—22no—
213C22×C11—82no—
214C22×C11—82no—
215C22×C11—82no—
216C22×C11—162no—
217C22×C11—162no—
218C22×C11#39211yescharacteristic
219C22×C11#44711yescharacteristic
220C22×C11#44812yes—
221C22×C11#44911yescharacteristic
222C22×C11#45412yes—
223C4×C11—21no—
224C4×C11—21no—
225C4×C11—44no—
226C4×C11—42no—
227C4×C11—82no—
228C4×C11—81no—
229C4×C11#44711yescharacteristic
230C4×C11#44911yescharacteristic
231C4×C11#46112yes—
232C4×C11#46611yescharacteristic
233C4×C11#46911yescharacteristic
234C4×C11#49211yescharacteristic
235C4×C11#49711yescharacteristic
236C22×Q8—21no—
237C22×Q8D4×C1111yescharacteristic
238C22×D4—21no—
239C22×D4—21no—
240C22×D4—21no—
241C2×SD16—24no—
242C2×SD16—42no—
243C2×SD16—42no—
244C22×C8—21no—
245C22×C8—21no—
246C22×C8—21no—
247C4⋊Q8—21no—
248C4⋊Q8—21no—
249C4⋊Q8—21no—
250C4⋊Q8—21no—
251C4⋊Q8—42no—
252C4⋊Q8—42no—
253#127—21no—
254#127—21no—
255#127—21no—
256#127D4×C1112yes—
257C4×Q8—21no—
258C4×Q8—21no—
259C4×Q8—21no—
260C4×Q8—21no—
261C2×C4⋊C4—24no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4D4×C1111yescharacteristic
265C2×C4⋊C4D4×C1112yes—
266C2×C4⋊C4D4×C1112yes—
267C2×C42—21no—
268C2×C42—21no—
269C2×C42C23×C1111yescharacteristic
270C4⋊C8—21no—
271C4⋊C8—21no—
272C4⋊C8—21no—
273C4⋊C8D4×C1112yes—
274#102—24no—
275#102—28no—
276#102—44no—
277C4×C8—21no—
278C4×C8D4×C1112yes—
279#95—24no—
280#95—21no—
281C2×C11—162no—
282C2×C11#162612yes—
283C2×C11#162712yes—
284C2×C11#199911yescharacteristic
285C2×C11#200311yescharacteristic
286C2×C11#201311yescharacteristic
287C24—41no—
288C2×Q8—21no—
289C2×Q8—21no—
290C2×Q8—21no—
291C2×Q8—21no—
292C2×Q8—21no—
293C2×Q8—41no—
294C2×Q8—41no—
295C2×Q8—41no—
296C2×Q8—41no—
297C2×Q8—41no—
298C2×Q8—41no—
299C2×Q8C11×D812yes—
300C2×D4—22no—
301C2×D4—22no—
302C2×D4—22no—
303C2×D4—44no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—41no—
307C2×D4—41no—
308C2×D4—42no—
309C2×D4—41no—
310C2×D4—41no—
311C2×D4—41no—
312C2×D4—42no—
313C22×C4—22no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—22no—
317C22×C4C2×D4×C1111yescharacteristic
318C22×C4C2×D4×C1111yescharacteristic
319C22×C4C2×D4×C1111yescharacteristic
320SD16—48no—
321C2×C8—22no—
322C2×C8—22no—
323C2×C8—42no—
324C2×C8—41no—
325C2×C8—41no—
326C2×C8—41no—
327C2×C8—42no—
328C4⋊C4—22no—
329C4⋊C4—21no—
330C4⋊C4—22no—
331C4⋊C4—21no—
332C4⋊C4—22no—
333C4⋊C4—48no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C4⋊C4C11×SD1614yescomplemented
339C42—41no—
340C42—41no—
341C42—41no—
342C42—41no—
343C42C2×D4×C1111yescharacteristic
344C42C2×D4×C1111yescharacteristic
345C42C2×D4×C1111yescharacteristic
346C42C11×#4111yescharacteristic
347C11#1005111yescharacteristic, direct product factor, Sylow
348C23—42no—
349C23—81no—
350C23—82no—
351C23—81no—
352C23—82no—
353C23C11×#12011yescharacteristic
354Q8—22no—
355Q8—22no—
356Q8—41no—
357Q8—41no—
358Q8—81no—
359Q8—81no—
360Q8—81no—
361Q8—81no—
362D4—44no—
363D4—42no—
364D4—42no—
365D4—44no—
366D4—82no—
367D4—81no—
368D4—81no—
369D4—81no—
370D4—81no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—24no—
374C2×C4—41no—
375C2×C4—42no—
376C2×C4—41no—
377C2×C4—42no—
378C2×C4—41no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4C11×#12011yescharacteristic
384C2×C4C11×#12011yescharacteristic
385C2×C4C11×#12111yescharacteristic
386C2×C4C11×#12111yescharacteristic
387C2×C4C11×#12111yescharacteristic
388C2×C4C11×#12711yescharacteristic
389C2×C4C2×C11×D811yescharacteristic
390C2×C4C2×C11×SD1612yes—
391C2×C4C11×#13511yescharacteristic
392C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
393C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
394C2×C4C11×#13712yes—
395C8—42no—
396C8—42no—
397C8—81no—
398C22—82no—
399C22—82no—
400C22—82no—
401C22—162no—
402C22—162no—
403C22C11×#39211yescharacteristic
404C22C11×#44711yescharacteristic
405C22C11×#44812yes—
406C22C11×#44911yescharacteristic
407C22C11×#45412yes—
408C4—21no—
409C4—21no—
410C4—44no—
411C4—42no—
412C4—82no—
413C4—81no—
414C4C11×#44711yescharacteristic
415C4C11×#44911yescharacteristic
416C4C11×#46112yes—
417C4C11×#46611yescharacteristic
418C4C11×#46911yescharacteristic
419C4C11×#49211yescharacteristic
420C4C11×#49711yescharacteristic
421C2—162no—
422C2C11×#162612yes—
423C2C11×#162712yes—
424C2C11×#199911yescharacteristic
425C2C11×#200311yescharacteristic
426C2C11×#201311yescharacteristic
subgroupG/H
center, socleC23×C11#120
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC2×C11×#127C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C11×#2546C2semidirect
5. C2×C11×#332C2semidirect
6. C2×C11×Q8⋊C8C2semidirect
7. C11×#1279C2semidirect
74. #10051C11direct (N × H)
126. C11×C4⋊C4SD16semidirect
137. #2546C2×C11semidirect
139. C2×#332C2×C11semidirect
140. C2×Q8⋊C8C2×C11semidirect
141. #1279C2×C11semidirect
338. C4⋊C4C11×SD16semidirect
347. C11#10051direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C11×#4862
C2×C11×#4602
C11×#25462
C11×#19822
C2×C11×#3322
C2×C11×Q8⋊C82
C11×#12792
#1005111